Optimal. Leaf size=25 \[ -7-\frac {e^2}{4}-\frac {e^{2 x}}{x}-3 x+x^2 \]
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Rubi [A] time = 0.04, antiderivative size = 17, normalized size of antiderivative = 0.68, number of steps used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {14, 2197} \begin {gather*} x^2-3 x-\frac {e^{2 x}}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-3+2 x-\frac {e^{2 x} (-1+2 x)}{x^2}\right ) \, dx\\ &=-3 x+x^2-\int \frac {e^{2 x} (-1+2 x)}{x^2} \, dx\\ &=-\frac {e^{2 x}}{x}-3 x+x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 0.68 \begin {gather*} -\frac {e^{2 x}}{x}-3 x+x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 18, normalized size = 0.72 \begin {gather*} x^{2} - 3 \, x - e^{\left (2 \, x - \log \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 19, normalized size = 0.76 \begin {gather*} \frac {x^{3} - 3 \, x^{2} - e^{\left (2 \, x\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 17, normalized size = 0.68
method | result | size |
default | \(x^{2}-3 x -\frac {{\mathrm e}^{2 x}}{x}\) | \(17\) |
risch | \(x^{2}-3 x -\frac {{\mathrm e}^{2 x}}{x}\) | \(17\) |
norman | \(x^{2}-3 x -{\mathrm e}^{2 x -\ln \relax (x )}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.49, size = 20, normalized size = 0.80 \begin {gather*} x^{2} - 3 \, x - 2 \, {\rm Ei}\left (2 \, x\right ) + 2 \, \Gamma \left (-1, -2 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.30, size = 15, normalized size = 0.60 \begin {gather*} x\,\left (x-3\right )-\frac {{\mathrm {e}}^{2\,x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 12, normalized size = 0.48 \begin {gather*} x^{2} - 3 x - \frac {e^{2 x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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